Sensor coordinate calibration in an ultrasound system

ABSTRACT

There is disclosed an embodiment for performing a calibration of a sensor by using an image registration between a three-dimensional ultrasound image and computerized tomography (CT) image. An ultrasound image forming unit includes an ultrasound probe and forms a three-dimensional ultrasound image of a target object. A sensor is coupled to the ultrasound probe. A memory stores a three-dimensional computed tomography (CT) image of the target object and position information on a position between the three-dimensional ultrasound image and the sensor. A processor performs image registration between the three-dimensional CT image and the three-dimensional ultrasound image to form a first transformation function for transforming a position of the sensor to a corresponding position on the three-dimensional CT image and performs calibration of the sensor by applying the position information to the first transformation function.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority from Korean Patent Application No. 10-2009-0070994 filed on Jul. 31, 2009, the entire subject matter of which is incorporated herein by reference.

TECHNICAL FIELD

The present invention generally relates to ultrasound systems, and more particularly to an ultrasound system and method for performing sensor coordinate calibration through image-based registration between a three-dimensional ultrasound image and a computerized tomography (CT) image.

BACKGROUND

The ultrasound system has become an important and popular diagnostic tool due to its non-invasive and non-destructive nature. Modern high-performance ultrasound imaging diagnostic systems and techniques are commonly used to produce two or three-dimensional images of internal features of patients (target objects).

However, the ultrasound system suffers from inherent shortcomings of an ultrasound image such as a low signal-to-noise ratio and a limited field of view. Thus, the image registration of a CT (or MR) image onto the ultrasound image has been introduced in order to compensate for deficiencies of the ultrasound image. A sensor has been used to perform the image registration of a CT (or MR) image onto the ultrasound image. Researches have been introduced to calibrate the sensor to match coordinates of the CT image and coordinates of the sensor.

Conventionally, after outer markers are attached on a surface of a target object, a CT image and an ultrasound image for the target object with the markers are acquired. Thereafter, the calibration is carried out by using a relationship between coordinates of the markers in the CT and ultrasound image. That is, the outer markers should be attached to the surface of the target objects before obtaining the CT image and the ultrasound image and be maintained in the same position until completing the acquisition of the ultrasound image. Moreover, a sensor must sense the positions of the respective outer markers.

Further, the registration between the coordinate of the CT image and the coordinate of the sensor has been performed by manually inputting inner markers on the CT image. Thus, a user of the ultrasound system had to input the inner markers, which causes the registration between the coordinate of the CT image and the coordinate of the sensor to be wrong.

SUMMARY

An embodiment for forming a plurality of three-dimensional ultrasound images is disclosed herein. In one embodiment, by way of non-limiting example, an ultrasound system, comprises: an ultrasound image forming unit including a ultrasound probe and being configured to form a three-dimensional ultrasound image of a target object; a sensor coupled to the ultrasound probe; a memory configured to store a three-dimensional computed tomography (CT) image of the target object and position information on a position between the three-dimensional ultrasound image and the sensor; and a processor configured to perform image registration between the three-dimensional CT image and the three-dimensional ultrasound image to thereby form a first transformation function for transforming a position of the sensor to a corresponding position on the three-dimensional CT image and perform calibration of the sensor by applying the position information to the first transformation function.

In another embodiment, a method of performing a calibration of a sensor, comprises: a) obtaining a three-dimensional ultrasound image of a target object obtained by the ultrasound system and a three-dimensional CT image; b) calculating a position information on a position between the three-dimensional ultrasound image and the sensor; c) performing registration between the three-dimensional ultrasound image and the three-dimensional CT image to obtain a first transformation function for transforming a position of the sensor to a corresponding position on the three-dimensional CT image; and d) performing calibration of the sensor by applying the position information to the first transformation function.

The Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used in determining the scope of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing an illustrative embodiment of an ultrasound system.

FIG. 2 is a block diagram showing an illustrative embodiment of an ultrasound image forming unit.

FIG. 3 is an illustrative embodiment of an ultrasound probe.

FIG. 4 is a block diagram showing an illustrative embodiment of a processor.

FIG. 5 is a schematic diagram showing an example of eigenvalues in the Hessian matrix.

DETAILED DESCRIPTION

A detailed description may be provided with reference to the accompanying drawings. One of ordinary skill in the art may realize that the following description is illustrative only and is not in any way limiting. Other embodiments of the present invention may readily suggest themselves to such skilled persons having the benefit of this disclosure.

FIG. 1 is a block diagram showing an illustrative embodiment of an ultrasound system which embodies the methods of the present invention. The ultrasound system 100 may include an ultrasound image forming unit 110, a sensor 120, a memory 130, a processor 140 and a display unit 150.

The ultrasound image forming unit 110 may be configured to transmit ultrasound signals to a target object (not shown) and receive ultrasound echo signals reflected from the target object. The ultrasound image forming unit 110 may be further configured to form a three-dimensional ultrasound image of the target object based on the received ultrasound echo signals.

FIG. 2 is a block diagram showing an illustrative embodiment of an ultrasound image forming unit 110. The ultrasound image forming unit 110 may include a transmit (Tx) signal generating section 111, an ultrasound probe 112 including a plurality of transducer elements (not shown), a beam former 113, an ultrasound data forming section 114 and an image forming section 115.

The Tx signal generating section 111 may generate Tx signals according to an image mode set in the ultrasound system 100. The image mode may include a brightness (B) mode, a Doppler (D) mode, a color flow mode, etc. In one exemplary embodiment, the B mode may be set in the ultrasound system 100 to obtain a B mode ultrasound image.

The ultrasound probe 112 may receive the Tx signals from the Tx signal generating section 111 and generate ultrasound signals, which may travel into the target object. The ultrasound probe 112 may further receive ultrasound echo signals reflected from the target object and convert them into electrical receive signals. In such a case, the electrical receive signals may be analog signals. The ultrasound probe 112 may be a three-dimensional probe, a two-dimensional probe, a one-dimensional probe or the like.

FIG. 3 is an illustrative embodiment of an ultrasound probe 112. At least one transducer element (not shown) of the ultrasound probe 112 generates an image plane IP, which is used to scan a region of interest ROI. The image plane IP may be one of slice planes of the three-dimensional ultrasound image. The sensor 120 is attached to the housing of the ultrasound probe 112 to determine the position and orientation of the image plane IP. The ultrasound system 100 coupled with the ultrasound probe 112 via the probe cable 105 can use the data generated by the sensor 120 to determine the position and orientation of the sensor 120 and/or the image plane IP, as described below.

In this preferred embodiment, the sensor 120 is a magnetic sensor that monitors the free-hand movement of the ultrasound probe 112 in six degrees of freedom with respect to a transducer element 170. As shown in FIG. 3, the sensor 120 and the transducer element 170 each define an origin (122, 172, respectively) defined by three orthogonal axes (X′, Y′, Z′ and X″, Y″, Z″, respectively). The sensor 120 monitors the translation of the origin 122 with respect to the origin 172 of the transducer element 170 to determine position and monitor the rotation of the X′, Y′, Z′ axes with respect to the X″, Y″, Z″ axes of the transducer element 170 to determine orientation.

The position and orientation of the sensor 120 can be used to determine the position and orientation of the image plane IP. As shown in FIG. 3, the image plane IP defines an origin OR defined by three orthogonal axes X, Y, Z, which are preferably aligned with the origin of a center acoustic line generated by the ultrasound probe 112. The position of the origin 122 and the orientation of axes X′, Y′, Z′ of the sensor 120 may not precisely coincide with the position of the origin OR and the orientation of the axes X, Y, Z of the image plane IP. For example, in FIG. 3, the origin OR of the image plane IP is offset from the origin 122 of the sensor 120 by a distance z₀ along the Z-direction and a distance of y₀ along the Y-direction. In FIG. 3, there is no offset along the X-direction nor is there a rotational offset in the orientation of the axes. Accordingly, the position and orientation of the sensor 120 do not directly describe the position and orientation of the image plane IP.

To determine the position an orientation of the image plane IP from the position and orientation of the sensor 120, sensor calibration data is used to transform the position and orientation of the sensor 120 to the position and orientation of the image plane IP. For simplicity, the term “position and orientation” is used to broadly refer to position and/or orientation. Accordingly, if the sensor 120 has the same orientation as the image plane IP, then the position and orientation calibration data may not contain any orientation calibration data. Similarly, as shown in FIG. 3, the sensor 120 may not have a positional offset with respect to one or more axes of the image plane IP.

There are a number of ways of defining the image plane/sensor offset. One method of calibrating at least some types of sensors use three orthogonal linear dimension offsets in X, Y, Z and three rotation angles about each of these axes. Other methods include using a position transformation matrix or quaternions, which are described in the user manual for the mini Bird™ and the Flock of Bird™ systems by Ascension Technology Corp.

As described above, the ultrasound probes with position and orientation sensors are typically used only with ultrasound systems that contain the calibration data for the probe/sensor pair. Conventionally, the probe/sensor pair is calibrated, and the calibration data is stored in the ultrasound system 100, which will be used in conjunction with the probe/sensor pair. If the probe/sensor pair is to be used with a different ultrasound system, then the probe/sensor pair typically needs to be re-calibrated on that different ultrasound system. Since sonographers are often unable or unwilling to perform probe/sensor pair calibration, probe/sensor pairs are often used only with the ultrasound system for which the probe/sensor pair was initially calibrated.

Referring back to FIG. 2, the beam former 113 may convert the electrical receive signals outputted from the ultrasound probe 112 into digital signals. The beam former 113 may further apply delays to the digital signals in consideration of the distances between the transducer elements and focal points to thereby output receive-focused signals.

The ultrasound data forming section 114 may form a plurality of ultrasound data by using the receive-focused signals. In one embodiment, the plurality of ultrasound data may be radio frequency (RF) data or IQ data. The image forming section 115 may form the three-dimensional ultrasound image of the target object based on the ultrasound data.

Referring back to FIG. 1, the sensor 120 may be mounted on one side of the ultrasound probe 112. In one embodiment, by way of non-limiting examples, the sensor 120 may be built in the ultrasound probe 112 to be away from the plurality of transducer elements (not shown) by a predetermined distance. Alternatively, the sensor 120 may be externally mounted on the ultrasound probe 112 to be away from the plurality of transducer elements. The sensor 120 may include three-dimensional sensor, which can detect a three-dimensional position and an angle of the ultrasound probe 112.

The memory 130 may store a three-dimensional CT image of the target object. In one embodiment, by way of non-limiting examples, the three-dimensional CT image may be a three-dimensional CT image of a liver in which a diaphragm and a blood vessel are extracted. The memory 130 may store information on a position between the three-dimensional ultrasound image and the sensor 120 (hereinafter, referred to as “position information”). The position information may include information on a distance between the transducer elements (not shown) and the sensor 120. In one embodiment, by way of non-limiting examples, the memory 120 may include at least one of a random access memory (RAM), a hard disk drive or the like.

The processor 140 may be configured to perform registration between the three-dimensional CT image and the three-dimensional ultrasound image, thereby forming a transformation function (T_(probe)) for representing the ultrasound probe 112 on the three-dimensional CT image. Furthermore, the processor 140 may perform calibration of the sensor 120 to match coordinates of the three-dimensional CT image (not shown) and coordinates of the sensor 120 based on the position information and the transformation function.

FIG. 4 is a block diagram showing an illustrative embodiment of the processor 140. The processor 140 may include a diaphragm extracting section 141, a vessel extracting section 142, a diaphragm refining section 143, a registration section 144, a calibration section 145 and an image processing section 146.

The diaphragm extracting section 141 may be configured to extract a diaphragm from the three-dimensional ultrasound image formed in the ultrasound image forming unit 110. In one embodiment, the diaphragm extracting section 141 may perform a Hessian matrix based flatness test upon the three-dimensional ultrasound image to extract the diaphragm. The diaphragm may be considered as a curved surface in the three-dimensional ultrasound image. Thus, regions in which a voxel intensity change in a normal direction at a surface is greater than a voxel intensity change in a horizontal direction at the surface may be extracted as the diaphragm. FIG. 5 is a schematic diagram showing an example of eigenvalues λ₁, λ₂ and λ₃ in the Hessian matrix.

Hereinafter, an operation of the diaphragm extracting section 141 will be described in detail. The diaphragm extracting section 141 may be configured to select voxels having a relatively high flatness value. The flatness μ(ν) may be defined as the following equation (1).

μ(ν)=φ₁(ν)φ₂(ν)/φ₃(ν)/φ₃ _(max) (ν)   (1)

wherein φ₁(ν), φ₂(ν) and φ₃(ν) in the equation (1) may be represented as the following equation (2).

$\begin{matrix} {{{\varphi_{1}(v)} = \left( {1 - \frac{\lambda_{1}(v)}{\lambda_{3}(v)}} \right)^{2}},{{\varphi_{2}(v)} = \left( {1 - \frac{\lambda_{2}(v)}{\lambda_{3}(v)}} \right)^{2}},{{\varphi_{3}(v)} = {\sum\limits_{i}^{\;}\; {\lambda_{i}(v)}^{2}}}} & (2) \end{matrix}$

wherein λ₁, λ₂ and λ₃ denote eigenvalues of the Hessian matrix at voxel ν. The flatness μ(v) may be normalized to have values ranging from 0-1. A flatness map may be formed based on the flatness values obtained from all of the voxels according to the equations (1) and (2). Thereafter, the voxels having a relatively high flatness value are selected. In one embodiment, the voxels having the flatness over 0.1 may be selected.

The diaphragm extracting section 141 may be further configured to perform the morphological opening upon the selected voxels to remove small clutters therefrom. The morphological opening may be carried out by sequentially performing erosion and dilation. That is, a predetermined number of the voxels are removed in the edges of the area in which the voxels exist, and thus, the area becomes contracted (erosion). In this manner, it becomes possible to remove small clutters. Thereafter, the edges of the area are expanded by the predetermined number of the voxels (dilation). These erosion and dilation may be performed by one or more voxels.

The diaphragm is the largest surface in the three-dimensional ultrasound image. The largest surface may be selected among candidate surfaces obtained by the intensity-based connected component analysis (CCA) for the voxles and the selected surface may be regarded as the diaphragm in the three-dimensional ultrasound image. The voxel-based CCA is one of the methods of grouping regions in which voxel values exist. For example, the number of voxels connected to each of the voxels through a connectivity test by referring to values of voxels neighboring the corresponding voxel (e.g., 26 voxels) may be computed. The voxels, of which connected voxels are greater than the predetermined number, are selected as candidate groups. Since the diaphragm is the widest curved surface in the ROI, the candidate group having the most connected voxels may be selected as the diaphragm. The surface of the diaphragm may be smoothened.

The vessel extracting section 142 may be configured to perform vessel extraction upon the three-dimensional ultrasound image. The vessel extracting section 142 may be configured to perform the vessel extraction through ROI masking, vessel segmentation and classification.

To avoid mis-extraction of the vessels due to mirroring artifacts, the ROI masking may be applied to the three-dimensional ultrasound image by modeling the diaphragm as a polynomial curved surface. For example, the ROI masking may he used to model the diaphragm as the polynomial curved surface by using the least means square. However, if all of the lower portions of the modeled polynomial curved surface are eliminated, then meaningful vessel information may be lost at a portion of regions due to an error of the polynomial curved surface. To avoid losing the vessel information, the lower portion of the modeled polynomial curved surface may be eliminated with a marginal distance. For example, the marginal distance may be set to about 10 voxels at a lower portion of the ROI mask.

Subsequently, the vessel extracting section 142 may be further configured to segment a vessel region and a non-vessel region. To exclude non-vessel high intensity regions such as the diaphragm and vessel walls, a low intensity bound value having a less reference bound value in the ROI masked three-dimensional ultrasound image may be set as a reference bound value. Thereafter, voxels with a higher intensity value than the reference bound value may be removed. The remaining regions may be binarized by using an adaptive threshold value. Then, the binarized segments may be labeled as vessel candidates.

Next, the vessel extracting section 142 may be further configured to remove non-vessel-type clutters from the binarization image to form real vessel regions from the vessel candidates. In one embodiment, the vessel classification may include a size test, which evaluates the quality of fit to a cylindrical tube, for filtering out tiny background clutters, a structure-based vessel test for removing non-vessel type clutters, i.e., an initial vessel test, a gradient magnitude analysis, and a final vessel test for precisely removing the clutters. Although some clutters are not removed through the structure-based vessel test, an initial threshold may be marginally set so that all vessels may be included. For example, a threshold value of the initial vessel test may be set to 0.6. At the final vessel test, clutters, which may he formed by small shading artifacts having low gradient magnitudes, may be precisely removed by considering variation of voxel values, i.e., gradient magnitudes, to thereby extract vessel data. In one embodiment, a threshold of the final vessel test may be set to 0.4.

The diaphragm refining section 143 may be configured to refine the diaphragm region by removing the clutters with the extracted vessel regions. The clutters are mainly placed near the vessel walls. For example, the vessel walls of inferior vena cava (IVC) are more likely to be connected to the diaphragm and cause clutters. These clutters may degrade the accuracy of the feature based registration, and thus, it may be necessary to refine the diaphragm region. To refine the diaphragm, the vessel regions are extracted according to the vessel extraction mentioned above, the extracted vessel regions may be dilated, and then the dilated vessel regions may be subtracted from the initially extracted diaphragm region to estimate vessel walls. The estimated vessel walls may be removed from the diaphragm region. Finally, the diaphragm region may be extracted by applying CCA and the size test.

The registration section 144 may be configured to perform the image registration between the three-dimensional ultrasound and CT image. The registration section 144 may extract sample points from the vessel regions and the diaphragm region, respectively, among the features extracted from the three-dimensional ultrasound image. Also, after the vessel regions and the diaphragm region are extracted from the CT image, the registration section 144 may extract sample points from the vessel and the diaphragm region, respectively. The image registration between the three-dimensional ultrasound and CT image may be performed based on the extracted sample points to thereby form the transformation function (T_(probe)) between the three-dimensional CT image and the three-dimensional ultrasound image. The transformation function (T_(probe)) may be given by a matrix and used to transform a position of the ultrasound probe 112 to a corresponding position on the three-dimensional CT image.

The calibration section 145 may perform the calibration of the sensor 120 based on the transformation matrix (T_(probe)) from the registration section 144 and the position information stored in the memory 130. More particularly, the calibration section 145 may form a transformation matrix (T_(sensor)) between the sensor 120 and the three-dimensional ultrasound image, i.e., a transformation matrix representing a position of the sensor 120 with respect to the three dimensional ultrasound image. The transformation matrix (T_(sensor)) may be given by a matrix. The transformation matrix (T_(sensor)) may be defined as the following equation (3).

$\begin{matrix} {T_{sensor} = {\begin{matrix} {r\; 11} & {r\; 12} & {r\; 13} & x \\ {r\; 21} & {r\; 22} & {r\; 23} & y \\ {r\; 31} & {r\; 32} & {r\; 33} & z \\ 0 & 0 & 0 & 1 \end{matrix}}} & (3) \end{matrix}$ r11=cos θy*cos θz+sin θx*sin θy*sin θz

r12=sin θz*cos θy−sin θx*sin θy*cos θz

r13=cos θx*sin θy,r21=sin θz*cos θx

r22=cos θz*sin θx,r23=sin θx

r31=sin θz+sin θ x*cos θy−cos θz*sin θy

r32=−cos θz*sin θx*cos θy−sin θz*sin θy

r33=cos θx*cos θy

wherein, x denotes coordinate of a lateral direction of the sensor 120, y denotes coordinate of an elevation direction of the sensor 120, z denotes an axial direction of the sensor 120, θ_(r) denotes an angle of the sensor 120 from the x-axis, θ_(y) denotes an angle of the sensor 120 from the y-axis, and θ_(z) denotes an angle of the sensor 120 from the z-axis. The elevation direction may be a swing direction of the transducer elements, the axial direction may be a scan line direction from the transducer elements and the lateral direction may be a longitudinal direction of the transducer elements.

The calibration section 145 may perform the calibration based on the transformation matrix (T_(probe)) and the transformation matrix (T_(sensor)). The calibration section 145 may form a transformation matrix (T) representing the position of the sensor 120 on the three-dimensional CT image. In one embodiment, the calibration section 145 may form the transformation matrix (T) through matrix multiplication of the transformation matrix (T_(probe)) and the transformation matrix (T_(sensor)).

The image processing section 146 may apply the transformation matrix (T) to the three-dimensional CT image to thereby form a two-dimensional CT image according to a two-dimensional ultrasound image.

Referring back to FIG. 1, the display unit 150 may display the two-dimensional CT image, which is provided from the processor 140. Furthermore, the display unit 150 may display the three-dimensional ultrasound image and the three-dimensional CT image.

Any reference in this specification to “one embodiment,” “an embodiment,” “example embodiment,” “illustrative embodiment,” etc, means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. The appearances of such phrases in various places in the specification are not necessarily all referring to the same embodiment. Further, when a particular feature, structure or characteristic is described in connection with any embodiment, it is submitted that it is within the purview of one skilled in the art to affect such feature, structure or characteristic in connection with other ones of the embodiments.

Although embodiments have been described with reference to a number of illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the spirit and scope of the principles of this disclosure. More particularly, numerous variations and modifications are possible in the component parts and/or arrangements of the subject combination arrangement within the scope of the disclosure, the drawings and the appended claims. In addition to variations and modifications in the component parts and/or arrangements, alternative uses will also be apparent to those skilled in the art. 

What is claimed is:
 1. An ultrasound system, comprising: an ultrasound image forming unit including a ultrasound probe and being configured to form a three-dimensional ultrasound image of a target object; a sensor coupled to the ultrasound probe; a memory configured to store a three-dimensional computed tomography (CT) image of the target object and position information on a position between the three-dimensional ultrasound image and the sensor; and a processor configured to perform image registration between the three-dimensional CT image and the three-dimensional ultrasound image to thereby form a first transformation function for transforming a position of the sensor to a corresponding position on the three-dimensional CT image and perform calibration of the sensor by applying the position information to the first transformation function.
 2. The ultrasound system of claim 1, wherein the target object includes a liver.
 3. The ultrasound system of claim 1, wherein the processor comprises: a diaphragm extracting section configured to extract a diaphragm region from candidate surfaces obtained by using a intensity-based connected component analysis (CCA); a vessel extracting section configured to extract vessel regions by removing non-vessel-type clutters from vessel candidates obtained by removing voxels of the three-dimensional ultrasound image having intensity value greater than a reference bound value; a registration section configured to extract sample points from the diaphragm region and the vessel regions and perform the image registration between the three-dimensional ultrasound and CT image based on the extracted sample points to thereby form the first transformation function; and a calibration section configured to perform calibration of the sensor to match coordinates of the CT image and coordinates of the sensor based on the first transformation function and the position information.
 4. The ultrasound system of claim 3, wherein the diaphragm extracting section is further configured to: obtain flatness values from voxels of the three-dimensional ultrasound image; select voxels having a flatness value greater than a reference value; remove a predetermined number of the voxels in edges of a area in which voxel values exist; expanding the edges by the predetermined number of the voxels; obtain the candidate surfaces from the voxels by the CCA; and select a widest surface among the candidate surfaces to extract the diaphragm region.
 5. The ultrasound system of claim 3, wherein the vessel extracting section is further configured to: model the diaphragm region to a polynomial curved surface in the three-dimensional ultrasound image to form a region of interest (ROI) mask; perform ROI masking by applying the ROI mask to the three-dimensional ultrasound image; form the vessel candidates by removing voxels having the intensity value greater than the reference bound value from the ROI masked three-dimensional ultrasound image; and extract the vessel regions by sequentially performing a size test, a structure-based vessel test, a gradient magnitude analysis, and a final vessel test for removing the non-vessel-type clutters from the vessel candidates
 6. The ultrasound system of claim 3, wherein the calibration section is further configured to: form a second transformation function between the three-dimensional ultrasound image and the sensor based on the position information; multiply the first transformation function by the second transformation function to form a third transformation function for representing the position of the sensor on the three-dimensional CT image; and perform calibration of the sensor based on the third transformation function.
 7. A method of calibrating an ultrasound system having an ultrasound probe and a senor, comprising: a) obtaining a three-dimensional ultrasound image of a target object and a three-dimensional CT image of the target object; b) calculating a position information on a position between the three-dimensional ultrasound image and the sensor; c) performing registration between the three-dimensional ultrasound image and the three-dimensional CT image to obtain a first transformation function for transforming a position of the sensor to a corresponding position on the three-dimensional CT image; and d) performing calibration of the sensor by applying the position information to the first transformation function.
 8. The method of claim 7, wherein the target object is a liver.
 9. The method of claim 7, wherein the step c) comprises: c1) extracting a diaphragm region from candidate surfaces obtained by using a intensity-based connected component analysis (CCA); c2) extracting vessel regions by removing non-vessel-type clutters from vessel candidates obtained by removing voxels of the three-dimensional ultrasound image having intensity value greater than a reference bound value; c3) extracting sample points from the diaphragm region and the vessel regions; and c4) performing the image registration between the three-dimensional ultrasound and CT image based on the extracted sample points to form the first transformation function.
 10. The method of claim 9, wherein the step c1) comprises: obtaining flatness from voxels of the three-dimensional ultrasound image; selecting voxels having a flatness greater than a reference value; removing a predetermined number of the voxels in edges of a area in which voxel values exist, expanding the edges by the predetermined number of the voxels; obtaining the candidate surfaces from the voxels by the intensity-based connected component analysis (CCA); and selecting a widest surface among the candidate surfaces to extract the diaphragm region.
 11. The method of claim 9, wherein the step c2) comprises: modeling the diaphragm region to a polynomial curved surface in the three-dimensional ultrasound image to form a region of interest (ROI) mask; performing ROI masking by applying the ROI mask to the three-dimensional ultrasound image; forming vessel candidates by removing voxels having a intensity value greater than a reference bound value from the ROI masked three-dimensional ultrasound image; and extracting the vessel regions by sequentially performing a size test, a structure-based vessel test, a gradient magnitude analysis, and a final vessel test for removing the non-vessel-type clutters from the vessel candidates.
 12. The method of claim 7, wherein the step d) comprises: d1) forming a second transformation function between the three-dimensional ultrasound image and the sensor based on the position information; d2) multiplying the first transformation function by the second transformation function to form a third transformation function for representing the position of the sensor on the three-dimensional CT image; and d3) performing calibration of the sensor based on the third transformation function. 